Question

Set of natural numbers, $A=\{x:xϵN\}$ is a proper subset of which of the following?

• A. Set of whole numbers, $A_1=\{x:xϵW\}$
• B. All of the above.
• C. Set of real numbers, $A_2=\{x:xϵR\}$
• D. Set of integers, $A_3=\{x:xϵZ\}$

Answer 1

The correct option is B

All of the above.

A set 'A' is said to be a proper subset of B if A is a subset of B and A $\ne$ B i.e if
(i) Every element of A is an element of B
(ii) B has at least one element which is not an element of A.

In all the options, the above conditions are satisfied. So, set of natural numbers 'A' is a proper subset of whole numbers, real numbers, and integers.